Fury captured the WBC belt in Las Vegas on Saturday with a seventh-round stoppage of Wilder and attention immediately turned to a unification bout with Joshua.
The WBA, WBO and IBF titles all belong to Joshua after he avenged his shock loss to Andy Ruiz Jr. with a points win in Saudi Arabia in December and Hearn has said Fury is the man his fighter wants next.
When Wilder was the WBC champion, a fight with Joshua proved too complicated to arrange, yet Hearn sees no issue now Fury is the belt-holder.
"I spoke to Top Rank and I spoke to MTK straight after the [Fury-Wilder] fight," Hearn told Sky Sports.
"Everybody's very clear on this, everybody wants this fight. Anthony Joshua, Tyson Fury, MTK, Top Rank, [Fury's promoter] Frank Warren, Matchroom.
"There's some hurdles to overcome but nothing too much. I promise you this fight will happen."
Wow unbelievable from Fury! Fair play and well done Sugar Hill and Andy Lee on first class game plan
— Eddie Hearn (@EddieHearn) February 23, 2020
He added: "You will get this fight. We will do everything that it takes to make this fight.
"Last time you had us and you had Team Wilder and we were locking heads. Right now you have two guys and two camps that genuinely want this fight, that genuinely will do everything they can. It is the only fight.
"We'd be clowns, idiots if we didn't make this fight."
Yet the possibility of that heavyweight clash occurring next appears highly unlikely as Wilder can exercise his right to a rematch and a third fight with Fury, the first ending in a draw in 2018.
Fury's promoter Frank Warren has already indicated he is expecting Wilder to want a trilogy fight with his boxer and Hearn admitted he would do likewise if he was part of the American's team.
"I don't want him to take the rematch but if you're asking me honestly, you have to take the rematch," added Hearn.
"If you don't take the rematch now, do you ever get your shot? Right now my money is on Wilder to rematch Tyson Fury.
"It's the timing, we don't mind waiting for the Fury fight until November, December but it must happen this year."
Hearn also revealed there are already firmed-up contingency plans in place for Joshua's next fight should Fury and Wilder meet in the ring again.
In that instance, IBF mandatory challenger Kubrat Pulev will fight Joshua at Premier League side Tottenham's stadium on June 20.
"We have an agreement in principle with Team Pulev," Hearn said.
"We're very close to a deal now with Spurs. That is our stadium of choice."
Photo Getty Images Caption: Anthony Joshua